What is the Fourier series representation of a signal x(n) whose period is N?(a) \(\sum_{k=0}^{\infty}|c_k|^2\)(b) \(\sum_{k=-\infty}^{\infty}|c_k|\)(c) \(\sum_{k=-\infty}^0|c_k|^2\)(d) \(\sum_{k=-\infty}^{\infty}|c_k|^2\)This question was addressed to me in quiz.I need to ask this question from Frequency Analysis of Discrete Time Signal in division Frequency Analysis of Signals and Systems of Digital Signal Processing

What is the Fourier series representation of a signal x(n) whose perio

1.	What is the Fourier series representation of a signal x(n) whose period is N?(a) \(\sum_{k=0}^{\infty}\|c_k\|^2\)(b) \(\sum_{k=-\infty}^{\infty}\|c_k\|\)(c) \(\sum_{k=-\infty}^0\|c_k\|^2\)(d) \(\sum_{k=-\infty}^{\infty}\|c_k\|^2\)This question was addressed to me in quiz.I need to ask this question from Frequency Analysis of Discrete Time Signal in division Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Correct choice is (B) \(\sum_{k=-\infty}^{\infty}\|c_k\|\) EXPLANATION: The average POWER of a periodic signal x(t) is given as \(\frac{1}{T_p}\int_{t_0}^{t_0+T_p}\|x(t)\|^2 dt\) =\(\frac{1}{T_p}\int_{t_0}^{t_0+T_p} x(t).x^* (t) dt\) =\(\frac{1}{T_p}\int_{t_0}^{t_0+T_p}x(t).\sum_{k=-∞}^∞ c_k^* e^{-j2πkF_0 t} dt\) By interchanging the positions of integral and summation and by applying the integration, we get =\(\sum_{k=-∞}^∞\|c_k \|^2\)

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